Precalculus: Mathematics for Calculus, 7th Edition

by
Stewart, James; Redlin, Lothar; Watson, Saleem

Chapter 5 - Secton 5.1 - The Unit Circle - 5.1 Exercises: 7

Answer

Yes, ($-\frac{\sqrt 5}{3},\frac{2}{3}$) is a point on the unit circle.

Work Step by Step

Since ($-\frac{\sqrt 5}{3},\frac{2}{3}$) is an (x, y) coordinate we can plug it into the equation of a circle, $x^{2}+y^{2}=1$.
$$(-\frac{\sqrt 5}{3})^{2}+(\frac{2}{3})^{2}=1$$ $$\frac{-\sqrt 5\times-\sqrt 5}{3\times3}+\frac{2\times2}{3\times3}=1$$ $$\frac{5}{9}+\frac{4}{9}=1$$ $$\frac{9}{9}=1$$ We end up with 1=1, which is true. Therefore, ($-\frac{\sqrt 5}{3},\frac{2}{3}$) is a point on the unit circle.